Normal functionals on Lipschitz spaces are weak$^\ast$ continuous

Ramón J. Aliaga, Eva Pernecká

Published 2020-04-29Version 1

Let $\operatorname{Lip}_0(M)$ be the space of Lipschitz functions on a complete metric space $M$ that vanish at a base point. We show that every normal functional in $\operatorname{Lip}_0(M)^\ast$ is weak$^*$ continuous, answering a question by N. Weaver.